Question

A solenoid is $2 \,m$ long and $3 cm$ in diameter. It has 5 layers of winding of 1000 turns each and carries a current of $5 A$. What is the magnetic field at its centre ? Use the standard value of $\mu_{0}$.

• A. $1.57 \times 10^{-4} T$
• B. $2.57 \times 10^{-3} T$
• C. $1.57 \times 10^{-2} T$
• D. $3.57 \times 10^{-6} T$

Answer 1

Answer: (C)

Length of solenoid, $l=2 \,m$
Total number of turns, $N =5 \times 1000=5000$
Number of turns per unit length,
$n =\frac{ N }{l}=\frac{5000}{2}=2500 \,m ^{-1}$
Current, $I =5\, A$
Now, $B=\mu_{0} nI =4 \pi \times 10^{-7} \times 2500 \times 5 T$
$=1.57 \times 10^{-2} T$